Limit of A
by Hikari of the Moon
Summary: L is the limit no one can reach. To think otherwise is just a mathematical error waiting to be corrected...  rated for character death and some butchering of calculus


**Author's Note:** Okay, so, this is my first fanfiction in about three years and first ever for Death Note. Yay for me. Inspired by a boring day in Calculus I. Betaed by the greatest person ever. You know who you are and I can't wait to see you again.  
**Warnings:** Character death (although not on-screen), calculus-level math, and the possible butchering of said calculus.  
**Disclaimer:** I do not own Death Note. Sad for me.

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A limit is loosely defined as the number f(x) gets closer to as x approaches a. You can get arbitrarily close to L, the limit, by getting x sufficiently close to a.

Math was so much simpler before it became metaphorical.

Limits are special because you can't ever reach it. When using that formula, you can only see everything close to L, never at it. L might be somewhere far above the line of the approaching numbers, or might not even be on the same plane. If so, the limit, L, does not exist.

A can never reach L. The closer you get to A, the closer you get to L. But A, top successor, isn't L. Won't ever be. And he might not even be close. The formula Whammy's House used might be wrong. Maybe a different one would fill the hole they tried to approach, or even let us reach it. But when everything went wrong, they did what all students do. They factored, tried to make it simpler, tried to force their solution to be right, even if it was wrong and couldn't be right.

But you can't factor a child. You can factor _in_ a child, in the least creepy way. People always take these things in the most perverted way possible. But what I mean is that you can factor in a child's life. His habits, his personality, his abilities, his personal limits—with a lowercase "l", not a capital "L"—and adjust your plans. They never did that for A.

A had to be closer, closer, just right, perfect. If he didn't fit, if they had to divide by zero to make him more like L, they'd factor out some undesirable thing to make him closer. Spending too much time playing with the other children? Isolate the variable. Lock him on his own floor, with only the other top students, the other children forced into the mold of L. Too concerned with his appearance? Restrict the domain. Don't let him eat, then he'll never get fat. But make him eat so he stays alive. No use being L if you're dead!

Hair getting in his way? Cut out the excess parts of the problem. A always had pretty hair, until they cut it all away. No more hair for A, not when it could be a distraction, could limit him from being L. But he never could be L, never ever. Because there's a limit to how close A can be to L and no matter how close you want to get, getting there may not even be possible. And if it is, you don't have A anymore. Only L.

What if some undesirable variable keeps sneaking in? A negative variable you can't seem to factor out, or an irrational number that just keeps going and going and going and going without ever stopping or making sense? It's how the problem works, it's best for the problem, but it makes it possible to solve. So, you break a rule. Or you look up a rule, one you haven't mastered because you've never had to work with limits before, or maybe you don't like them. You don't like math, but need to because it's your job to mold these variables and make them reach that limit.

So they separate us. Factor me out and away from him. And that's great, because now there's no other variable besides A and what they want to do to him. I'd sneak in, and the first time he hugged me and cried like a little girl and told me he felt sick and hurt and hungry and scared and oh so alone. The second time he pretended I wasn't there, even when I cut his weak little arm to prove it. The third time is now. Now, now, now.

I can do math too.

I see numbers everywhere. I always know the limits.

Life has a limit. You approach it but you never know what or where it is, you just have to test it by living! Sometimes it's far away, sometimes it's close, and sometimes it's too close. Suddenly you've hit the limit and poof. Gone. I tried, tried to do the math. Worked on my formula, worked so hard, tried to find the limits. Tested it on old people, fixed the formula when it didn't work. Saw a child on the street once, whose limit was almost upon her. I gave her an ice cream cone and told her to enjoy it. She dropped it in the street, stood still too long, and bam! Car. Blood. Body flying. Dead.

Not my fault. Maybe it wouldn't have been that car, but she would have died then. Maybe it would've veered onto the sidewalk. Maybe a robber would've stabbed her. Her limit was there and no matter what path she took, life would deliver her to death. But it didn't have to hurt so much. She got to taste the sweetness of that strawberry ice cream before she died. A good last moment, I'd say. Better if it was jam, but still good.

A was not so lucky.

Now, on my third visit to this little cell, oh excuse me, I mean, _study room_, all white and he didn't even pick a way to die that would've given some color to the walls. His lips match his eyes now, though, the room's only color. Blue. Sickly, pale blue. Hung himself from that stupid ceiling fan. They only put it there so the stillness wouldn't drive him mad, but it only went around forever, never going anywhere, just following the blade before it.

I didn't plan on following him. Maybe A's weight would snap the blade, ruin the fan. Maybe the stupid people running this kiddie prison will realize he couldn't be L, would never be L, because L was L and A was A. A always liked math too, because 1 was never 2, 5 was never 9, and numbers fit patterns and no one tried to make 13 into 12.

A wouldn't mind if I left them a message, would he?

Cut his wrist, take a little blood, smear it all over the walls so everyone would know. "A DOES NOT EQUAL L". A pretty little solution to this problem. They can make us arbitrarily as close as they want, but we'll never be L. They can drive people closer to A, closer to being so desperate, so close to the limit but close enough to see the hole in the graph that they'd rather factor themselves out of life and off the plane of existence. As they get closer to A, what they become in the end is closer to L. That's what they want, Roger and Whammy and maybe even L himself. But it's the other way around. The symbols are backwards, the problem inverted, never right.

The closer we get, the more we're driven to be L, the closer we'll get to being A. Dead by our own hands, a new hole in the graph they'll cover up by factoring him out. Pretending the limit can be reached this way when the universe, when the rules say it can't.

They pick new little variables from the young children and shove them into a new formula, and see if they get L that way. Too bad, so sad, the limit doesn't exist. L doesn't exist. Not if I have anything to say about it, anyway.


End file.
